A car was purchased for $3,495 and will depreciate 20% each year.
Find a linear function for the value of the car at time t in years. Define variables clearly.
Graph the function you found in part A.
A claim is made that the car will not be worth anything in five years. Do you agree with this claim? Explain. In your explanation include the following:
State the problem in your own words.
Describe the strategy used to solve the problem.
Clearly state your answer and explain why it is reasonable.
Tell whether you agree with the claim, explaining why or why not
3495 *.8^t
.8^5 = .328 or about $1150 which is not nothing but is also not much
Problem:
A car was purchased for $3,495 and it will depreciate by 20% each year. We need to find a linear function for the value of the car at time t in years. Then, determine if the claim that the car will not be worth anything in five years is reasonable.
Variables:
Let V(t) represent the value of the car at time t in years.
Strategy:
To find the linear function for the value of the car at time t, we need to determine how much the value decreases each year. Since the car depreciates by 20% each year, we can calculate the value of the car at any given time using the formula:
V(t) = Initial Value - (Depreciation Rate * Initial Value) * t
The initial value of the car is $3,495, and the depreciation rate is 20% (or 0.2).
V(t) = 3495 - (0.2 * 3495) * t
To determine whether the claim that the car will not be worth anything in five years is reasonable, we need to substitute t = 5 into the linear function and evaluate the result.
Answer:
The linear function for the value of the car at time t is V(t) = 3495 - (0.2 * 3495) * t.
To find the value of the car in five years (t = 5), substitute t = 5 into the function:
V(5) = 3495 - (0.2 * 3495) * 5
V(5) = 3495 - (0.2 * 3495) * 5
V(5) = 3495 - 0.2 * 3495 * 5
V(5) = 3495 - 0.2 * 17475
V(5) = 3495 - 3495
V(5) = 0
The value of the car after five years is $0. This means that, according to the linear function, the car will not be worth anything in five years.
Therefore, based on the given information and the linear function, I agree with the claim that the car will not be worth anything in five years.